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Rav Hutner allowed it because he felt there is no real true simcha from taped Music that will bring you to dancing and since that is the reason for the Issur he allowed it during sefira.By extension of the same logic Reb Shlomo Zalman in his sefer on Pesach allows Chazunis and classical music too of course he adds it is better to be stringent.Reb Pinchas Schinberg has the most intriguing approach and basically says that today most people are in depressive moods and need the Music as a refuah so therefore there is no Issur ever.Just as interesting extension of the music on sefias Haomer I saw recently that Reb Sternbach does not allow Accpella music but allows Music for exercising.

R' Moshe Feinstein basically prohibits music year-round, and he explicitly writes that there's no distinction between live or canned music. I've always heard that (at least for American Jewry), our custom to abstain from music during Sefira is to follow R' Moshe Feinstein's view for this period (though we don't the rest of the year). Hence a reason to prohibit live or canned. Rabbi Moshe Bleich also has a piece about music during Sefira in Tradition, c. ~2009.
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ShalomApr 18 '10 at 23:42

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It is not Reb Moshe its a Halacha and a gemara in Kesbous.
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SimchasTorahApr 19 '10 at 0:03

The reason Shulchan Aruch does not discuss music during sefira is because as YS said, it is a Halacha that it is forbidden year round because of the destruction of the temple. However that being said what is mentioned as forbidden year round is "micholos urikudim", basically dance music. I heard that Rav Yasha Ber Soloveitchik permitted classical music during sefira and the three weeks (as well as year-round) because of this reasoning. The article in Tradition is excellent.
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YahuApr 19 '10 at 3:13

Even though the Mehaber does forbid music all year long there are dissenting opinions. I remember seeing in a more recent reponsum that much of the Torah observant world relies on the dissenters. Hence allowing for concerts and other instances of non-wedding dancing and music.
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YahuApr 22 '10 at 19:45